3.2 Right-angled and non-right-angled trigonometryIB Maths: Analysis and Approaches SL: Flashcards

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$\sin\theta$, $\cos\theta$, $\tan\theta$ in a right-angled triangle?

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$\sin\theta$ , $\cos\theta$ , $\tan\theta$ in a right-angled triangle?: $\frac{\text{opp}}{\text{hyp}}$ , $\frac{\text{adj}}{\text{hyp}}$ , $\frac{\text{opp}}{\text{adj}}$
State the sine rule.: $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$
State the cosine rule for a side.: $c^2=a^2+b^2-2ab\cos C$
State the cosine rule for an angle.: $\cos C=\frac{a^2+b^2-c^2}{2ab}$
Area of a triangle using sine?: $\frac12ab\sin C$ , with $C$ the angle between $a$ and $b$
When do you use the sine rule?: When you know a side and its opposite angle, plus one other side or angle.
When do you use the cosine rule?: Two sides and the included angle, or all three sides.
What does a negative cosine tell you about an angle in a triangle?: It is obtuse (between $90^\circ$ and $180^\circ$ ).
Triangle with sides 8, 5 and included angle $60^\circ$ : third side?: $\sqrt{64+25-40}=7$
Exact $\sin60^\circ$ and $\cos60^\circ$ ?: $\frac{\sqrt3}{2}$ and $\frac12$
Why does a median split a triangle into equal areas?: The two parts have equal bases and share the same perpendicular height.
Right-angled at $B$ , $AB=5$ , $BC=12$ : $\cos A$ ?: $\frac{5}{13}$